Discrete Mathematical Structures, Sixth Edition, offers a
clear and concise presentation of the fundamental concepts of discrete
mathematics. Ideal for a one-semester introductory course, this text contains
more genuine computer science applications than any other text in the field.
The focus on computer science prepares students for future computer
This book is written at an appropriate level for a wide variety of
majors and non-majors, and assumes a college algebra course as a
The emphasis on proof lays the foundation for mathematical thinking.
Clear organization of topics prevents students from being
overwhelmed. The authors treat relations and digraphs as two aspects of the same
fundamental idea, which is then used as the basis of virtually all the concepts
introduced in the book.
Vignettes of mathematical history open each chapter, providing
students with a practical background of how these ideas were developed.
Additional number theory coverage provides more information on the
properties of integers, including base n representations, and gives more
contexts for isomorphism.
Cryptology is explored throughout the book, introducing students to
this exciting field.
Coverage of coding provides students with a full picture of all of
its aspects, including efficiency, effectiveness, and security. A set of coding
exercises for each chapter is also included in Appendix C.
Exercises emphasize multiple representations of concepts, and provide
practice on reading and writing mathematical proofs.
Experiments provide opportunities for in-depth exploration and
discovery, as well as for writing and for working in groups. Topics include
weighted voting systems, Petri nets, Catalan numbers, and others.
End-of-chapter material includes Tips for Proofs, a summary of Key
Ideas, and a Self-Test, which contains a set of conceptual review questions to
help students identify and synthesize the main ideas of each
New to This Edition
New sections on Logic, Mathematical Statements, and Logic and Problem
Solving help students understand proofs and proof techniques. Additional
exercises help students develop conjectures and how to prove or disprove them.
More applications, exercises, and figures have been added to help
students learn and retain the material.
New material on fuzzy sets and fuzzy logic introduces students to a
topic that is extremely important for modern issues of automated feedback and
control of processes.
Popular puzzles like Sudoku and their underlying mathematical
connections form a continuous thread in the text, connecting set theory, Boolean
matrices, algorithms and coding, logic, the general construction of proofs,
coloring problems and polynomials, and other topics in a way that students will
find both interesting and instructive.
Table of Contents
4. Relations and Digraphs
6. Order Relations and Structures
8. Topics in Graph
9. Semigroups and Groups
10. Languages and Finite-State
11. Groups and Coding